Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices

• Autores: Malcolm Brown, Marco Marletta, Sergey N. Naboko, Ian Wood
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 3, 2008, págs. 700-718
• Idioma: inglés
• DOI: 10.1112/jlms/jdn006
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• Resumen

  • Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between the M-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where the M-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where the M-function corresponds to the Dirichlet to Neumann map.